Mathematical apparatus



' Oct. 9, 192's. A. H. KENNEDY MATHEMATICAL APPARATUS Original Filed Feb. 13. 1921 INVENTOR.

Fat-ranted Set. 9, 192.3,

tinirsnsrarss ALBERT H. KENNEDY, or nooxronnmnmne.

MATHEMATICAL APPARATUS.

Application filed February 18,1921,Seria1 No. 446,112. Renewed June 11, 1923.

To all whom it may concern:

Be it known that I, ALBERT H. KENNEDY, a citizen of the United States, a resident of Rockport', in the county of Spencer and State of Indiana, have invented a new and improved mathen'iatical apparatus for the purpose of generating an infinite number of right-angled triangles upon a common hy-v potenuse, together 'with' squares upon the other two sides, making in all positions complete and exact diagrams of the Pythagorean proposition. V I attain this object by means ofthe mechanism illustrated in the accompanying draw ing, which shows its 'plan'and operation.

In the present position of the mechanism,

1-2-3 represents a right angled triangle 1 41 5-2 represents the square upon the hypotenuse, 13- 7'6 represents the square upon the longer leg and 23,-8 9 represents the square upon the shorter leg.

The lines in the figure represent wires,

bars ofsteel, brass, or any other rigid mate rial.

The bars about the square 1--452, are made rigid at the corners, sothat it may retain its shape.

The two bars 1.10and 114 are fastened V rigidly'together at right angles and are pivoted at 1.

The two bars 2-15 and 213 are likewlse tastened rigidly together at right angles and r are pivoted at 2. The bars 13, 10-15 and 101 -14 hold these two systems at right angles to each other in any possible pov sition. as they are rotated. about the points,

parallelograms, pivoted at the four corners 1 and 2. The bars 1015, 1-2 and 13-44 are all equal to each other. 16 and 17 are the corners of the square 121716.

The bar 6-12 is pivoted at 16 and kept parallel to 114 by the connecting bar 121 which is equal to'116.

Likewise the bar 9-11 is pivoted at 17 and kept parallel to 27 by the connecting bar 11-15' which is equal to 2- 17.

The bars 12-14 and 11,15 are each equal to the bar 116 It is obvious that in this manner the two pairs of hinged parallelograms 1-2-13-1 1,

11-15 are thus connected into one system 7 at right angles t0 each other and, that the system is rotated to the right or left on n Win also be noticed that 1-24. at

right angled triangle in any and every po-v Y sition and has squares generated upon its two legs while the square uponthe hypote nuse remains constant It will also be noticed that the system Z is rotated toward the right, the square l6-7"3 grows larger and larger as'the square 2-.3'8'9 grows smaller and smaller until it disappears and the. square 1+6'73 becomes equal to 1--2--5'-4, the square upon the hypotenuse.

In like manner, when the system is r0- tated toward V the left the reverse becomes 1 true. V K

The members of this system of parallelograms may be extended below, so as to-ro-' tate about the four corners'of the square 116172, but the results would be the same. 'Also the parallelograms may be extendedbelow and be connected with addi-' tional parallel members as above, but it' WOUlClbB-ill all'respects identical with the plans. and functions above I described. Whether the square on the hypotenuse is below it,- as shown by 1-2-5--4, or above it,

- as shownby 1--'16- 172-, inakes 'no differ ence in the plan or the functions performed.

. I claim as my invention: r V- 1. The combinatlon of two pairs of hmged of a square and 'connectedand functioning in such a manner that when rotated about these four points, the two pairs of paralleh.

ograms will remain at right angles to eaclii I other in'all possible positions, substantially as described. 7

2. The combination of two pairsof hinged parallelograms, pivoted at the four corners of a square, so connected and functioning, that when rotated about the four points,-

they'will generate right angled triangles in all possible positions, with one side of the said-square as a'common hypotenuse, substantially as set forth.

77 3. The combination of two'pairs of hinged v to one side of the said square, substantially parallelograms, pivoted at the four corners as described. of a square, and s0 connected and functioning, that When rotated about these four H; KENNEDY 5 points, they Will generate in all possible po- Witnesses:

sitionsr two SQ-HELEGS .upon the legs, of. .a right :BERTHA HIGGINS,

anglebtriangle, Whose hypotenuse ,isi- -e que1 V O. P, M. THURMAN., 

